Is there a mathematical notion of "why"? That is, are there reasons behind the truth of certain mathematical statements? Personally, my belief is that true mathematical statements just are true. There are no reasons behind them. In fact, the notion of "reasons why a certain mathematical statement is true" does not even make sense to me. But perhaps some mathematician or philosopher has rigorously defined a notion of "why". If so, I would like to see such a text.
2026-03-27 10:09:16.1774606156
Is there a mathematical notion of "why"?
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One idea comes from Plato's world of forms (see Plato's Republic), that the reason we can reason about things logically is because our cognition dips into this world of forms. For example, we don't really deal with circles in this world, only approximations, but that in the cognitive world of forms our minds can grasp a real circle, the form of the circle and that reasoning about circles is just our minds exploring this world of forms.
The why of mathematical truth is thus: because there exists a cognitive world of forms we can dip into. But then, why does such a world exist? There are lots of ideas, but none of them are satisfying in that we feel like we have reached a bottom ground fundemental truth that all other truths are built on. Perhaps that bottom ground fundemental truth is just that things are because they are, as proposed.